Corollary 3

Tag 0DO6, permanent. Cite it as [Bourbaki, Tag 0DO6].

Algebra, chapter IX, § 10. Angles

The group $S^+/H$ is commutative. It operates on the set of non-isotropic lines of $E$ . Whatever the non-isotropic lines $D, D'$ of $E$ , there exists one and only one element $\varphi$ of $S^+/H$ such that $D' = \varphi(D)$ .

This follows from Corollary 1 and from the fact that $H$ leaves every line of $E$ globally invariant.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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